Everton confirmed they have paid £28million for the 21-year-old and Lukaku has signed a five-year contract on a estimated £75,000-a-week.
Lukaku spent last season on loan at Goodison Park and was their leading scorer with 16 goals in 33 appearances, helping the club finish fifth.
The transfer smashes Everton's previous transfer record, which was £15m for another Belgian, Marouane Fellaini.
Manager Roberto Martinez made the striker one of his primary summer targets but the player's involvement in the World Cup and extensive negotiations with Chelsea have taken time.
Lukaku joined Chelsea from Anderlecht in 2011, nearly double Everton's previous transfer record, which was £15m for another Belgian, Marouane Fellaini.
It caps a great week for Everton who also tied Ross Barkley down to a new four-year-contract.
Lukaku said: “I am really excited about rejoining Everton. I had a fantastic experience last season and a great relationship with the manager, the chairman, the staff, the players and the fans. I can’t wait to get started again and I’m looking forward to a successful season.”
Lukaku will wear the number 10 shirt at Goodison Park and will return to the club for Leon Osman's testimonial on Sunday against Porto after a few days back in Belgium.
Manager Martinez said: "Welcoming Romelu Lukaku back to Everton on a permanent basis is the news that all Evertonians wanted to hear.
"We know that Romelu is still a young man and the potential that he has is quite unique, and we are desperate to see him enjoying his football and to watch him grow as footballer in the years to come.
"The arrival of Rom is more than just a signing, it's the fruition of a lot of hard work to get the player we wanted. This is a big moment for Everton's history and the perfect way of getting the squad ready for the start of the season.”
Chairman Bill Kenwright added: "Romelu was a massive part of the jigsaw for Roberto and Everton and nobody is more pleased than me that an 11-month quest ended at lunchtime today, thanks hugely to the efforts of all parties, including Rom, his representative, Chelsea and, of course, Roberto."
He becomes Everton's third signing of the season after Gareth Barry and Muhamed Besic.
Lukaku is undoubtedly one of the best young strikers, with a physique and presence that belies his tender years. He has only just turned 21, is intelligent, strong, quick and can finish - but Mourinho doesn't seem to like him, probably for personal reasons.
What is most surprising is not that the player is leaving Chelsea, but that a. he is not moving to one of Europe's bigger clubs, and b. the size of the fee, which is remarkable for an Everton which previously struggled to balance the books. It is something of a coup for the Toffees - who will fancy their chances of making the top four.
Romelu Lukaku of Everton celebrates his goal (Getty Images)
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